Calculating Coordinate Transformation Error

For two sets of 3D point clouds, the transformation error between them can be calculated using Euclidean distance. Transformation error refers to the distance deviation between point sets caused by various factors during coordinate transformation. To minimize this error, different coordinate transformation methods can be employed, such as least squares fitting and singular value decomposition (SVD) approaches. The least squares method typically involves minimizing the sum of squared residuals between corresponding points, while SVD provides a robust solution for finding the optimal rotation matrix. Additionally, preprocessing of the original point clouds is essential before coordinate transformation, including outlier removal using statistical methods like Z-score or IQR filtering, and coordinate normalization through mean-centering or scaling operations. These steps significantly improve the accuracy and stability of coordinate transformation, with practical implementations often utilizing point cloud registration algorithms like Iterative Closest Point (ICP) combined with error metric calculations.